New Mathematical Tools in Direction Finding and Spectral Analysis

Linear Algebra (i.e., the algebra of vector spaces) provides widely used mathematical tools and concepts which are today being considered for implementation in special compute architectures. It seems that so many signal processing problems can be expressed and, more importantly, implemented efficiently as a sequence of vector and matrix operations, that a signal processing system with a capability for high speed linear algebra is necessary if the more advanced signal processing algorithms are to be implemented to operate in real time. The purpose of this paper is to support the notion that linear algebra is a sound basis for important signal processing system implementations and, further, to suggest that multilinear algebra (i.e., the algebra of vector, bivector, trivector, etc. spaces) offers an even broader set of signal processing "tools". Examples and ideas from direction finding and time series analysis are discussed.